Modulus of Rupture.
Moment of diminished section = moment of i rivet + moment of 2 rivets
(a - (£4- £•)}# = *5x arrrn-^xarm
_ (1-394* 8-5)-h(49'i6x 11-25) „
- 68-28 -(13-94 -4- 49-1 6) **
yc being limiting stress (see below), B c and D E are reference
lines, and the areas are found as before.
Each stress area = 26*35 an<^ arm = 2 x"12
For W. I. plate girders t/t= 5 and/c =4.
For Steel plate girders /t= 6 and/c = 5
The reduced jfc being an allowance for buckling.
.•. Moment of resistance =/c x area x arm
= 4 x 26*35 x 3i '12 = 2226 ton, ins, for W. I.
= 5 x 26*35 x 21 §i2 = 2782 ton, ins, for Steel
Value of f in Beams.— If a < solid' beam be broken
.across, the ultimate stress, -deduced by applying the momenta!
formula, will be usualty- found much greater than ft breaking.
If then, the bending theory be pushed as far as the breaking
load, we must meet the case by the value
where /0 is the stress found by transverse experiment and called
the moduhis of rupture, while O we shall call the bending coefficient.
It varies with the beam section. Thus :
In sections ^ or ^ O- is greatest, being about 2
In sections | or H O is less, being about ij-
In sections *TT O = r
but depends also on the material, as seen in the following table
^compiled from experiment), and is often less than unit/ for woods.
TABLE OF BENDING COEFFICIENTS (0) FOR SOLID SECTIONS.
Fir | -52 to -94
Oak | 7 to i *o
Pitch Pine 1 '8 to 2-2
Cast Iron | 2; • 2-35;
Wrought Iroa | 1*6; • 175
Forged Steel | 1-47; • i'6
Gun Metal | i -o; • i '9
«• ^ ) where ^=flange width
and &=wtb tkickness
And our beam formula becomes Bm = OfZ*